2
1
Various species of Eucalyptus have been of in­ terest in California since their introduction in
1860 (Metcalf, 1924), with Eucalyptus globulus
(Blue Gum) being the most widely planted. While its wood has limited use as lumber, its rapid growth has caused it to be favored as windbreaks and ornamentals. The recent increase in demand for firewood and a growing market for hardwood fiber has caused renewed interest in planting eucalyptus.
The purpose of this article is to present a model for growth of Eucalyptus globulus and to use this model to generate variable site-density yield tables. These yield tables are then used to determine optimum stocking levels and rotation length under various site conditions. This model deals solely with biological growth and does not con­ sider economic implications of stand establishment and management.
The models derived represent unmanaged stands only. Certain management practices increase site quality and some means of assessing this increase must be applied in order for the models to be mean­ ingful under intensive management conditions.
Within this article, the following topics are discussed:
-- The source, limitations, and adjustments made to the data used to generate the model.
-- A description of the model itself and how it
1
Presented at the Workshop on Eucalyptus in
California, June 14-16, 1983, Sacramento,
California.
2
Staff Research Associate and Statewide Forestry
Specialist, respectively, Cooperative Extension,
University of California, Berkeley, California.
Gen. Tech. Rep. PSW 69. Berkeley, CA: Pacific Southwest Forest and Range
Experiment Station, Forest Service, U.S. Department of Agriculture; 1983.
Abstract: A study of the major Eucalyptus globulus stands throughout California conducted by Woodbridge
Metcalf in 1924 provides a complete and accurate data set for generating variable site-density yield models. Two models were developed using linear re­ gression techniques. Model I depicts a linear rela­ tionship between age and yield best used for stands between five and fifteen years old. Model II de­ picts a sigmoidal relationship between age and yield with slightly poorer statistical fit but greater reliability beyond fifteen years of age. Significant independent variables used in Model I are: initial plantation density; site index; and an interaction variable consisting of age x site index. Significant independent variables in Model II are: natural log of initial plantation density; site index; and inverse age. Variable site and density yield tables are developed from Model II for stands under mini­ mal management. Culmination of mean annual incre­ ment occurs at age ten under all conditions. Assum­ ing a goal of maximization of mean annual increment of merchantable cordwood, planting densities of
435, 680 and 1210 trees per acre are recommended for low, medium, and high sites respectively._ is used to generate variable site-density yield tables.
-- Conclusions drawn from analysis of the yield tables.
-- Suggestions for further analysis and research.
THE DATA
The data used in this analysis was gathered by
Louis Margolin in 1910 (Margolin, 1910) and by
Woodbridge Metcalf in 1924 (Metcalf, 1924) in their studies of the major Blue Gum stands in California.
As described in his article, in order to generate site and yield functions, Metcalf used data collec­ ted in these two studies, which included a total of
96 stands. This data was adjusted to result in the data set used in the current analysis.
The Metcalf and Margolin Data
Location of Stands
Stands were located in 19 counties throughout
California, from Arcata in Humboldt County to
Escondido in San Diego County, representing a wide variety of soil and climatic conditions.
Information Collected
Information collected for each stand includes the following:
-- Stand age
-- Initial plantation density in trees per acre
-- Surviving trees per acre
61

-- Average diameter, height, and volume of surviving trees
-- Volume per acre in cubic feet and cords
-- Soil and water characteristics
Also, in order to develop a measure of site quality, height was measured on the tallest 10 percent of trees in most of the stands.
Methods of Collection
Selection of Plots--In the data collected by
Metcalf, "one or more of the rows running through representative portions of the stand" were selected for measurement. The method of row selection was not described and therefore randomness of the sampling procedure is not assumed.
In the Margolin data, sample areas were ¼-acre plots within the interior of each grove. Usually only one such plot was taken per stand and these were selected to show average conditions. This method of plot selection is not random and could result in bias toward higher yield.
Surviving Trees Per Acre--Metcalf states that
"each surviving tree" was measured, as well as blank spaces and "scrubby trees." A scrubby tree is not defined and no lower diameter limit is given for surviving trees. In assessing trees per acre at time of measurement, one must assume that none of the "scrubby" trees are survivors of the original plantation.
In the Margolin study, all trees with dbh of l½ inches or more were measured. As with the
Metcalf data, one must assume that trees less than
1½ inches dbh were not counted as survivors of the original plantation.
Average Diameter of Surviving Trees--In the
Metcalf data, since "scrubby" trees are assumed not to be survivors, it must also be assumed that the distribution of diameters of surviving trees has some lower diameter limit. Since we do not know what this limit is, it is difficult to assess the amount of variation around the average dia­ meter. Diameters measured by Margolin, however, were recorded by 1-inch diameter class, giving a diameter distribution, or stand table, for each stand sampled.
Height of Surviving Trees--Total heights, in­ cluding stump and top were measured for as many trees as possible. A height-diameter curve was derived in order to estimate heights on trees not measured.
Calculation of Volume--Volumes were calculated using the following formula:
V = BA x H x ff x TPA where: V = Volume in cubic feet per acre
BA = Basal area in square feet of the
62 average single tree.
(BA = [Average Diameter/24]
2
)
H = Total height of the average single tree ff = Form factor relating stem volume to
(BA x H). Stem volume is from the top of a one-foot stump to a minimum diameter of two inches at the top.
TPA = Number of surviving trees per acre at time of measurement
Site Classification
In order to develop a height-age relationship as a measure of site quality, Metcalf measured the tallest 10% of the trees sampled and plotted heights of these dominant trees against age. Groves in which overcrowding was thought to have interferred with height growth were not included. In all,
Metcalf included 45 of the Metcalf groves and 26 of the Margolin groves in his site classification.
An average age-height curve was drawn through the data and harmonized curves were drawn to intersect with maximum and minimum values. The area between the maximum and minimum curves was then divided into three zones, labeled Site I, II, and
III. Figure 1 represents the Metcalf site classi­ fication curves.
Figure 1 -- Metcalf Site Classifications
The Current Data Set
Adjustments
The following adjustments were made in the above data to result in the data set used in the analysis.

Elimination of Observations--Only those stands for which the height of dominant trees was recorded are included, thus eliminating 20 of the stands.
An additional stand was eliminated because it had been thinned.
Addition of Observations--Eight of the Metcalf stands were measured twice at different points in time. Metcalf used only the first measurement in his estimation of site. The current data set in­ cludes the eight remeasurements, with the assump­ tion that site remains constant over time. A total of 78 stands are included in the current data set.
Volume Estimation--The method used by Margolin to estimate volume was not specified other than by reference to volume tables. In order to merge the two data sets, volumes for Margolin stands were recalculated using the formula noted above.
Developing a Site Index Measurement
Metcalf's site quality measure resulted in site ratings of I, II, or III. In order to be consistent with other yield studies for Eucalyptus globulus, a site index was developed from Metcalf's age-height curves in figure 1, using a base age of 10. The following table represents the relation between
Metcalf's site class and the site index derived from it.
Table 1 -- Site Class-Site Index Relationship
Site
Class
Site Index
(Height of Dominants at 10 Years)
I
II
III
Greater than 93
65 to 93
Less than 65
40. Models should not be used for extrapolation beyond age 40. This limitation is not significant for commercially-grown stands since harvest is likely to occur prior to age 15.
ANALYSIS
Analytical Systems Used
Linear regression analysis was performed using the Statistical Analysis System -- General Linear
Model (SAS-GLM) program package.
Yield Models
The analysis yields two production models with statistically significant fit. The first gives a linear plot of predicted yield against age. The second gives a plot of predicted yield against age which more closely approximates a sigmoidal bio­ logical production function which one might an­ ticipate. Figure 2 depicts these models for a given site and initial plantation density. Both models can be used, given certain constraints, as ex­ plained below.
Site indices for the stands in the data set ranged from a low of 41 to a high of 118.
The method used was to locate age and height of dominants for a given stand on figure 1 and then to follow a harmonized curve through that point to its intersection with the base age 10 reference line. For instance, a dominant height of 126 feet at age 25 would equate to a site index of 82. In this way, figure 1 can be used to determine site index for any stand where age and height of domi­ nants are known.
Range of Ages
The ages of stands in the current data set ranged from 2 to 40 years. Only 12 (15.4 percent) of the stands were in excess of 15 years of age.
Models derived from this data show best fit in younger age classes and caution must be used in estimating volume in age classes between 15 and
Figure 2 -- Model I and Model II Yields
63

Model I
Model Form--Model I takes the form of:
Y = -3177.17 + 1.70(TPA1) + 29.47(SI) + 3.77(AGSI) where: Y = Yield in cubic feet per acre
TPA1 = Initial plantation density in trees per acre
SI = Site index in feet at age 10
AGSI = Age x site index
Analysis of Variance--Table 2 presents the analysis of variance for Model I.
Analysis of Variance--Table 3 presents the analysis of variance for Model II.
Table 3--ANOVA - Model II
Source of Sum of
Variation Squares T F R
2
C.V.
Intercept
SI 1
1nTPA1 1
1/A 1
Residuals 12.54
Total
5.80
Table 2-- ANOVA - Model I
Source of Sum of
Variation Squares T R
2
C.V
Note that while the statistics for Model I are slightly better than those for Model II, the dif­ ferences are relatively minor. The lower C.V. for
Model II is a result of the dependent variable be­ ing a logarithm. Exponentiating results in a co­ efficient of variation similar to that of model I.
Intercept
TPA1
SI
AGSI
Residuals
Total
-4.28
1 3.19 x 10
7
3.07
1 30.15 x 10
7
2.95
1 53.34 x 10
7
18.95
74 11.04 x 10
7
77 97.72 x 10
7
2
) of .887 and the coefficient of variation (C.V) of 34.6.
Discussion--Schumacher (1939) and Clutter (1963) suggested methods of generating linear models to express nonlinear production functions by transforming dependent and independent variables into natural logarithms. Model II is essentially the
Clutter model using 1nTPA1 rather than Clutter's
In of Basal Area. Discussion -- Because site index appeared to have a greater effect on yield with increasing age, an interaction variable consisting of Age x Site was anticipated. As indicated by its high T value relative to other variables, AGSI is the most sig­ nificant independent variable. This is logically sound since, with a given initial plantation den­ sity, site quality will have a strong effect on rate of growth while total volume will vary most directly with age.
As shown in figure 2, when lnY is transformed back to cubic foot yield and plotted against age, the result is close to the expected sigmoidal curve. Since the Clutter-based model gives nearly as good a fit as Model I with greater confidence when using the model for stands older than 15 years, this model was used to generate subsequent yield tables.
While this model gives a good prediction of vol­ ume within the range of most of the data, it does not give an intuitive depiction of growth, as shown by figure 2. The linear relationship between age and yield results from the fact that 80 percent of the data falls between the ages of 5 and 15, the linear range of the anticipated sigmoidal function.
This data so weights the model in this form that statistical significance is high even though the model is linear.
Model II
Model Form--Model II takes the form of:
Variable Site-Density Yield Tables
In generating yield tables under varying site and initial stocking conditions, one will wish to know average diameter of the stand as a measure of merchantability, as well as total yield. A dia­ meter of two inches is generally considered to be the lower merchantable limit for cordwood and the diameter distributions shown in the Margolin data indicate that for an ASD of six inches, virtually all trees in the stand will be in excess of two inches dbh. The expression for average diameter of the stand is: lnY = 4.86449 + .02547(SI) + .34896 (lnTPA2) -
10.41628(I/A)
AD =
BA
TPA2 x .00545 where: AD = Average diameter of the stand in inches
BA = Basal area per acre in square feet
TPA2 = Surviving trees per acre where: lnY = The natural log of yield in cubic feet per acre
SI = Site index in feet at age 10 lnTPAI = The natural log of initial stocking density in trees per acre
I/A = Inverse age
64
In order to predict AD, then, it is necessary to construct models for basal area and surviving trees.

Basal Area Model
Because basal area is also a measure of produc­ tion, it is logical that BA could be predicted by the same independent variables as cubic foot yield.
The following model results: lnBA = 2.07854 + 0.496(SI) +.33354(lnTPA1) -
6.55518(I/A) where: lnBA = Natural log of basal area per acre
SI = Site index in feet at age 10
TPAl = Initial stocking in trees per acre
I/A = Inverse age
The correlation coefficient for this model is .79.
Affective coefficient of variation is about 40.0. stocking, and age. Tables 4a-c are representative tables for SI = 60, 85, and 105 and initial stock­ ing of 680 trees per acre.
Variable Site Yield Functions
By plotting yield against age for a given stock­ ing level under varying site conditions, one may see graphically how yield varies with site. Fig­ ure 3 represents yield with initial plantation density of 680 under three site conditions.
DISCUSSION
Refer to table 4 and figure 3 for the following discussion.
Surviving Trees Per Acre
The only significant predictor of surviving trees per acre is initial stocking density, which gives the following model: where: TPA2 = Surviving trees per acre
TPA1 = Initial stocking in trees per acre
While R
2
for this model is only .54, it is acceptable since it is used only to calculate a rough estimate of the average diameter of the stand.
TPA2 = 183.69 + .56 TPA1
Explanation and Interpretation of Yield Tables
Surviving Trees Per Acre (TPA2)
Note that TPA2 varies only with TPA1 and that mortality occurs immediately. This indicates that survival is linked with establishment and that once established, the stand remains stable over time.
When initial stocking is 300 trees per acre,
TPA2 exceeds TPA1. This may be loosely explained by sprouting on under-utilized sites, though this explanation is somewhat weak. As noted earlier, the mortality issue is clouded by problems in interpreting the data as well as by ingrowth from sprouts and volunteers. TPA2 is a rough estimate of survival.
Final Yield Tables
The final yield tables were generated by com­ bining the three models derived above and iterat­ ing through variations in site index, initial
Table 4a--Yield Table (SI = 60, TPA1 = 680)
SITE INDEX = 60 TREES/ACRE: Initial = 680; Surviving = 519
Age
Average
Diameter
Basal ea
Yield Mean Annual Incr. Current Annual Incr.
(years) (inches) (Ft 2 /Ac) Ft 3 /Ac Cds/Ac Ft 3 /Ac/Yr Cds/Ac/Yr Ft 3 /Ac/Yr Cds/Ac/Yr
2
4
6
8
10
12
14
16
18
20
25
30
35
40
1.5
3.4
4.5
5.2
5.6
5.9
6.2
6.4
6.5
6.6
6.9
7.0
7.1
7.2
6.5
33.5
57.9
76.1
89.7
100.0
108.1
114.6
120.0
124.4
132.9
138.8
143.2
146.6
31.8
3261.5
3455.8
3835.2
4111.0
.4
4.8
11.4
17.6
22.8
27.1
30.7
33.7
48.0
49.8
15.9
107.6
170.9
197.8
205.3
203.5
197.5
189.6
181.2
172.8
153.4
137.0
123.4
112.1
.2
1.2
1.9
2.2
2.3
2.3
2.2
2.1
2.0
1.9
1.7
1.5
1.4
1.2
199.3
297.4
278.5
235.3
194.6
161.2
134.7
113.8
97.2
75.9
55.2
41.8
32.7
2.2
3.3
3.1
2.6
2.2
1.8
1.5
1.3
1.1
.8
.6
.5
.4
65

Table 4b--Yield Table (SI = 85, TPA1 = 680)
SITE INDEX = 85 TREES/ACRE: Initial = 680; Surviving = 519
Average Basal Yield Mean Annual Incr. Current Annual Incr.
Age Diameter
(years) (inches) Ft 2
Area
/AC Ft 3 /Ac Cds/Ac Ft 3 /Ac/Yr Cds/Ac/Yr Ft 3 /Ac/Yr Cds/Ac/Yr
2
4
6
8
10
12
1.8
4.1
5.5
6.3
6.8
7.2
9.5
48.8
84.2
60.2
813.5
1937.9
110.6
130.3
145.4
.7
9.0
33.2
43.1
51.3
30.1
203.4
323.0
373.9
388.1
384.7
14
16
18
20
25
30
35
40
7.5
7.7
7.8
8.0
8.3
8.4
8.6
8.7
157.2
166.6
174.4
180.9
193.1
201.7
208.1
213.1
5225.8
5735.1
6165.3
6532.6
7249.8
7771.1
8166.3
8475.8
58.1
63.7
68.5
72.6
80.6
86.3
90.7
94.2
373.3
358.4
342.5
326.6
290.0
259.0
233.3
211.9
.3
2.3
3.6
4.2
4.3
4.3
4.1
4.0
3.8
3.6
3.2
2.9
2.6
2.4
376.6
562.2
526.5
444.8
367.9
304.7
254.7
215.1
183.7
143.4
104.2
79.0
62.0
4.2
6.2
5.9
4.9
4.1
3.4
2.8
2.4
2.0
1.6
1.2
.9
.7
Average Diameter of the Stand (AD)
This variable behaves as one might expect, increasing with age and site index, but decreasing as initial plantation density increases.
Yield (YFT3)
Gives volume at various ages.
Cords
Gives volume in cords where:
CORDS = YFT3/90
66
Table 4c--Yield Table (SI = 105, TPA2 = 680)
SITE INDEX = 105
Age
(years)
Average
Diameter
(inches)
Basal
Yea
(Ft /AC)
TREES/ACRE: Initial = 680; Surviving = 519
Yield Mean Annual Incr. Current Annual Incr.
Ft 3 /Ac Cds/Ac Ft 3 /Ac/Yr Cds/Ac/Yr Ft 3 /Ac/Yr Cds/Ac/Yr
2
4
6
8
10
12
14
16
18
20
25
30
2.1
4.8
6.3
7.3
7.9
8.3
8.7
8.9
9.1
9.3
9.6
9.8
35
40
10.0
10.1
8697.2
9544.9
235.2
280.7
287.4
100.1
1353.9
3225.1
4977.8
6458.5
7682.9
243.9
260.5
272.1
13591.1
14106.2
50.1
338.5
537.5
622.2
645.8
640.2
96.6
106.1
114.0
120.8
134.1
143.7
151.0
156.7
570.1
543.6
482.6
431.1
388.3
352.7
.6
3.8
6.0
6.9
7.2
7.1
6.9
6.6
6.3
6.0
5.4
4.8
626.9
935.6
876.3
740.3
612.2
507.1
423.8
358.0
4.3
3.9
305.6
238.6
173.6
131.6
103.0
7.0
10.4
9.7
8.2
6.8
5.6
4.7
4.0
3.4
2.7
1.9
1.5
1.1
Mean Annual Increment (MAIFT3 and MAICD)
Gives mean annual increment in cubic feet and cords per acre per year, where:
MAI = Yield/Age
Note that for all variations of site and initial stocking, MAI culminates at age 10. Thus, for maximum biomass production, given the two-inch mer­ chantability standard for volume determination, harvest will occur at about age 10.

Figure 3--Yield-Age
.
Relationships Varying Site
Index (TPA1 = 680)
Current Annual Increment (CAIFT3 and CAICD)
Gives current year's growth in cubic feet and cords. Note that CAI culminates at age 6, somewhat before MAI, as one would anticipate. Note also that at culmination of MAI, MAI approximately equals CAI, again as one would expect.
Recommended Planting Densities
Assuming a goal of maximum merchantible cordwood, the yield tables generated from the models in this analysis can be used to determine optimal spacing for any given site. Optimal spacing will be that which yields highest. MAI at age 10 with minimum ASD of 6 inches. Table 5 represents recom­ mended planting density to achieve this goal for a range of site indices.
NEEDS FOR FURTHER RESEARCH
Site Quality - Soil Correlation
The above analysis assumes that a 10-year site index for Eucalyptus globulus is known at time of planting. If Blue Gum has not been grown before
Table 5 -- Recommended Planting Densities for
Maximum Merchantable Cordwood
Site Index Recommended Planting Density
55 TPA
60 435
65 435
75 680
85 680
95 1210
105 1210
115 1210 on the site, and if there are no stands growing on similar sites available for comparison, this assumption may not be met. E. globulus appears to grow best on well-drained, sandy-loamy soils with a 10- to 12-foot water table. This relationship between edaphic-climatic-geomorphological con­ ditions and site index requires further research so a site index may be estimated prior to plant­ ing.
For the present time, individuals who wish to use these models and yield tables to assess growth and yield can use some general observations of the soil-site quality relationship provided by Metcalf.
This information is shown in table 6.
Table 6 -- Relationship Between Site Index and
Soil-Site Characteristics
Approximate
Site Index Soil-Site Characteristics
Greater than 93 . Soils - loamy-sandy loam
- deep bottomland
. Agricultural quality -- high
. Water table -- near surface during most of the year
. Slope - flat
65-93 . Soils - sandy-sandy loam
. Agricultural quality -- fair to good under irrigation
. Water table -- low; irrigation required
. Slope -- medium to flat
Less than 65 . Soils - sandy, adobe
. Agricultural quality - low
. Water table - low; irrigation infeasible
. Slope - steep
. Windy
Older Stands
As noted earlier, the data analyzed was heavily weighted to stands 5 to 15 years old, making ex­ trapolation of the model to older stands somewhat risky. Similar data should be gathered for stands
15-60 years old to see if a better fit can be obtained.
67

Economic Analysis
This analysis assumes that maximum biomass production is the only management goal. Costs of site preparation, irrigation, fertilization and harvest are not considered; nor are projected stumpage prices or (demand for fuelwood or chips.
Further analysis should combine biological growth potential with economic factors to give a return on investment analysis for Eucalyptus globulus plantations.
REFERENCES
Connell, M.G.R.; Smith, R.I. Yields of minirotation closely spaced hardwoods in temperate regions: review and appraisal. Forest Science 26(3);
1980.
Clutter, Jerome L. Compatible growth and yield models for loblolly pine. Forest Science 9(3);
1963.
Eucalypts for Planting. Food and Agriculture
Organization of the United Nations, Rome; 1979.
Margolin, Louis, Yield from eucalyptus plantations in California. California State Board of
Forestry, Bulletin N.17 1910.
Metcalf, Woodbridge. Growth of eucalyptus in
California plantations. University of California
College of Agriculture, Agric. Exper. Station,
Bulletin N.380; November 1924.
Schumacher, F.X.; Coile, T.S. Growth and yield of natural stands of the southern pines. T.S.
Coile, Inc.; 1970.
68